NMAK17011U Algebraic Number Theory
(AlgNT)

Algebraic number fields and their rings of integers, trace,
norm, and discriminants, prime decomposition in Dedekind domains
and rings of integers, prime decomposition in quadratic and
cyclotomic number fields, decomposition theory in Galois
extensions, decomposition- and inertia groups and fields, quadratic
reciprocity via decomposition theory, Frobenius automorphisms, the
prime divisors of the discriminant and ramification, finiteness of
class numbers, Dirichlet's unit theorem, the first case of
Fermat's last theorem for regular primes.